[tex]C_{2019}^1-C_{2018}^2-C_{2018}^1 = \\ \\ =\dfrac{2019!}{1!(2019-1)!}-\dfrac{2018!}{2!(2018-2)!}-\dfrac{2018!}{1!(2018-1)!} = \\ \\ = \dfrac{2019!}{2018!}-\dfrac{2016!\cdot 2017\cdot 2018}{2(2016)!}-\dfrac{2018!}{2017!} = \\ \\ = \dfrac{2018!\cdot 2019}{2018!}-\dfrac{2017\cdot 2018}{2}-\dfrac{2017!\cdot 2018}{2017!} = \\ \\ = 2019-2017\cdot 1009-2018 = \\ \\ =1 - 2017\cdot 1009 = -2035152[/tex]
